INFINITE SEMIPOSITONE PROBLEMS WITH INDEFINITE WEIGHT AND ASYMPTOTICALLY LINEAR GROWTH FORCING-TERMS

In this work, we study the existence of positive solutions to the singular problem -Delta(p)u = gimel m(x)f(u) - u(-alpha) in Omega, u = 0 on partial derivative Omega, where gimel is positive parameter, Omega is a bounded domain with smooth boundary, 0 < alpha < 1, and f : [0, infinity] -> R is a continuous function which is asymptotically p-linear at infinity. The weight function is continuous satisfies m(x) > m(0) > 0, vertical bar vertical bar m vertical bar vertical bar(infinity) < infinity. We prove the existence of a positive solution for a certain range of gimel using the method of sub-supersolutions.